A Local Constraint Resolution Approach for Dynamics Modeling of Parallel Kinematic Manipulators With Single-Loop Complex Limbs

Abstract

Abstract A large class of parallel kinematic manipulators (PKM) possess complex limbs, i.e. limbs that comprise kinematic loops. This paper addresses the modeling of PKM with complex limbs with a single closed loops. The best known representative is the Delta robot. A systematic approach to the kinematics and dynamics modeling has been proposed recently. The remaining open issue was the computationally efficient solution of the geometric loop constraints. This is particularly important for model-based control of PKM. Global solution of the overall system of constraints is not efficient. In this paper, a local constraint resolution is introduced. A nested iteration scheme is applied for the local constraint resolution. This implements a constraint embedding technique, as a special case of the general concept known for multibody systems. Among others, one advantage is that the method allows dealing with redundant constraints locally or may even avoid them. As an example, the method is applied to the well-known Delta robot. This PKM is modeled as a 3R[2UU] PKM, which is known to be overconstrained. It is shown that the local constraint embedding can deal with this redundancy.